The fifth-generation (5G) of cellular networks and beyond requires massive connectivity, high data rates, and low latency. Millimeter-wave (mmWave) communications is a key 5G enabling technology to meet these requirements thanks to its technical potentials that can be integrated with other 5G enablers such as ultra-dense networks (UDNs) and massive multiple-input-multiple-output (massive MIMO) systems. However, some technical challenges, which are mainly related to specific characteristics of mmWave propagation, must be addressed. All the aforementioned points will be discussed in this article before presenting the different existing architectures of massive MIMO mmWave systems. This survey mainly aims at presenting a comprehensive state-of-the-art review of the channel estimation techniques associated with the different mmWave system architectures. Subsequently, we will provide a comparison among existing solutions in terms of their respective benefits and shortcomings. Finally, some open directions of research are discussed, and challenges that wait to be met are pointed out.